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### Course: MAP Recommended Practice > Unit 55

Lesson 4: Summarizing center of distributions (central tendency)- Statistics intro: Mean, median, & mode
- Mean, median, & mode example
- Mean, median, and mode
- Missing value given the mean
- Missing value given the mean
- Impact on median & mean: removing an outlier
- Impact on median & mean: increasing an outlier
- Effects of shifting, adding, & removing a data point
- Choosing the "best" measure of center

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# Mean, median, & mode example

Here we give you a set of numbers and then ask you to find the mean, median, and mode. It's your first opportunity to practice with us! Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- I really have a hard time remembering the differences between these three. Does anyone have a suggestion like a riddle or rap etc. to help me to remember the three?(377 votes)
- Here is what we use in class:

Hey diddle diddle,

The median is the middle

You add and divide for the mean

The mode is the one that appears the most

And the range is the difference in between(1,042 votes)

- I have a question with regard to the mode (3:33):

I can understand it if there is one number which appears most, but what if you have 2 numbers that appears as much?

For example: 1,2,2,4,4,7,8

What's the mode in this case?(182 votes)- All your answers are great, but my accelerated math teacher says that you can have more than one mode.(41 votes)

- can ther be more than 1 mode(50 votes)
- yes their can be more than one it's just you have to find the number in between them.(25 votes)

- Please vote on this. I need some votes for badges(29 votes)
- What happens if there are two different numbers that apperar the same number of times? For example, 08767424(5 votes)
- You can have more than on mode, it this case there are two - 7 and 4 (called bimodal).(21 votes)

- i dont under stand what it is asking it makes no sense can you make it more simple(7 votes)
- Mean = Average

Median = Middle, and if you have 2 numbers in the middle, find the mean of those 2 numbers

Mode = Most common number(16 votes)

- What happens when two same numbers, example 23 and 23 are the Median, what would be the answer??(6 votes)
- The median is the middle number in a data set. If there are two "middle" numbers, you take their average. So, for your problem, the median is 23.(8 votes)

- I dont get mode(5 votes)
- Mode is most, so you need to find the most common on the list. Did that help answer your question?(7 votes)

- How do you find mode when no numbers repeat(4 votes)
- If no numbers repeat (and there is more than one number) then most would consider the set to have no mode**. This would also be the case for something like { 2, 2, 2, 3, 3, 3, 8, 8, 8} where all numbers appear an equal number of times.

** I have seen some texts that would say all the numbers would be modes in this case, but that is not the typical definition.(10 votes)

## Video transcript

Find the mean, median,
and mode of the following sets of numbers. And they give us the
numbers right over here. So if someone just
says the mean, they're really
referring to what we typically, in everyday
language, call the average. Sometimes it's
called the arithmetic mean because you'll
learn that there's other ways of actually
calculating a mean. But it's really you just
sum up all the numbers and you divide by the
numbers there are. And so it's one way of
measuring the central tendency. The average, I
guess, we could say. So this is our mean. We want to average
23 plus 29-- or we're going to sum 23 plus 29 plus
20 plus 32 plus 23 plus 21 plus 33 plus 25, and then divide
that by the number of numbers. So we have 1, 2, 3,
4, 5, 6, 7, 8 numbers. So you want to divide that by 8. So let's figure out
what that actually is. Actually, I'll just get the
calculator out for this part. I could do it by hand, but
we'll save some time over here. So we have 23 plus 29 plus
20 plus 32 plus 23 plus 21 plus 33 plus 25. So the sum of all
the numbers is 206. And then we want
to divide 206 by 8. So if I say 206 divided
by 8 gets us 25.75. So the mean is equal to 25.75. So this is one way
to kind of measure the center, the
central tendency. Another way is with the median. And this is to pick out the
middle number, the median. And to figure out the
median, what we want to do is order these numbers
from least to greatest. So it looks like the
smallest number here is 20. Then, the next one is 21. There's no 22 here. Let's see, there's two 23's. 23 and a 23. So 23 and a 23. And no 24's. There's a 25. 25. There's no 26, 27, 28. There is a 29. 29. Then you have your 32. 32. And then you have your 33. 33. So what's the middle number
now that we've ordered it? So we have 1, 2, 3,
4, 5, 6, 7, 8 numbers. We already knew that. And so there's actually
going to be two middles. If you have an even
number, there's actually two numbers
that qualify for close to the middle. And to actually get the median,
we're going to average them. So 23 will be one of them. That, by itself,
can't be the median because there's
three less than it and there's four
greater than it. And 25 by itself
can't be the median because there's three larger
than it and four less than it. So what we do is we take the
mean of these two numbers and we pick that as the median. So if you take 23 plus 25
divided by 2, that's 48 over 2, which is equal to 24. So even though 24 isn't
one of these numbers, the median is 24. So this is the middle number. So once again, this
is one way of thinking about central tendency. If you wanted a number
that could somehow represent the middle. And I want to be clear,
there's no one way of doing it. This is one way of
measuring the middle. Let me put that in quotes. The middle. If you had to represent
this data with one number. And this is another way of
representing the middle. Then finally, we can
think about the mode. And the mode is
just the number that shows up the most
in this data set. And all of these numbers show
up once, except we have the 23, it shows up twice. And since because 23 shows up
the most, it shows up twice. Every other number shows
up once, 23 is our mode.